U.S. Pat. Nos. 5,653,643 and 5,944,617 disclose vibration absorbing material which is particularly useful when applied to the gripping area of the handle of some type of implement such as a golf club or various types of other athletic equipment or tools. The material described in those patents is of single layer form having certain characteristics with regard to its friction, vibration dampening and hardness features. It would be desirable if variations could be provided for such material which would enhance the characteristics of the material without significantly resulting in a material which is of impractical thickness. Ideally, such material should provide a sting free grip which could be readily adapted to the handle of various types of implements such as athletic equipment, tools and handlebars.